The \(2\nu \)  double-electron capture in \(^{190}\) Pt can undergo to several
excited levels of \(^{190}\) Os (see Fig. REF ). In this
case, in addition to X-rays cascade, \(\gamma \) -peaks at the energy
of the excited level (in the transition to the first \(2^+\)  186.7
keV excited level) and also at the energies of the transitions
between the initial and final levels of the daughter are expected.
To estimate \(\lim S\)  value for a possible 186.7-keV peak area, the
experimental spectrum was fitted in the energy interval \(176-194\) 
keV by a model consisting of a straight line, peaks of \(^{235}\) U
and \(^{226}\) Ra with energies 185.7 keV and 186.2 keV,
respectively, and a Gaussian peak at 186.7 keV with the width
fixed according to the formula (REF ) to describe the
effect searched for. The fit returns a 186.7-keV peak area
\(S=-28(39)\)  counts, that corresponds to \(\lim S=39\)  counts
following the recommendations [1]}. A part of the
energy spectrum gathered with the Pt sample in the vicinity of
\(\gamma \)  peak 186.7 keV expected in the \(2\varepsilon \)  decay of
\(^{190}\) Pt to the \(2^+\)  186.7 keV excited level of \(^{190}\) Os is
presented in Fig. REF . The half-life limits for the
transitions to higher excited levels of \(^{190}\) Os were obtained
in a similar way. The limits are presented in Table
REF .
<FIGURE>